一种含噪声不确定多输入多输出非线性时变系统的最优跟踪控制

An optimal tracking control for uncertain multiple-input multiple-output non-linear time-varying systems with noises

如何在确保实时性能的前提下,将系统耦合、随机因素、时变特性和不确定非线性的影响一同最小化具有重要意义.为此,本文提出了一种基于自适应多维泰勒网(MTN)的优化控制方案,包括MTN控制器(MTNC)和MTN滤波器(MTNF).首先,设计基于强化学习和自适应动量因子的改进梯度法来调节MTNC权值以快速响应被控对象的不确定性和时变特性,实现最优控制;证明闭环系统稳定性.而后,通过Lyapunov稳定性理论设计MTNF权值更新律,使动态误差指数收敛到零;恰当选择Lyapunov函数来构造具有全局最小值的能量空间并对MTNF的Lyapunov特性进行分析;证明MTNF误差的收敛速度和收敛区域,避免奇点问题.最后,仿真结果表明所提出的控制器和滤波器可在较短的时间内获得更高的精度.

It is of great significance to minimize the effects of system coupling, stochastic factors, time-varying characteristics, and uncertain nonlinearity while ensuring real-time performance. Therefore, we propose an optimization control scheme based on adaptive multidimensional Taylor network(MTN), comprising a MTN controller(MTNC) and a MTN filter(MTNF). Firstly, an improved gradient method, which is based on reinforcement learning and adaptive momentum factor, is designed to adjust the MTNC weights to respond quickly to the uncertainty and time-varying characteristics of the controlled object to achieve the optimal control. The stability of the closed-loop system is proved. Then, the MTNF weight update law is designed by Lyapunov stability theory, and the dynamic errors exponentially converge to zero. The Lyapunov function is appropriately selected to construct the energy space with the global minimum value and the Lyapunov characteristics is analyzed. The convergence speed and convergence area of MTNF error are proved, and the singularity problem is avoid. Lastly, simulation results show that the proposed controller and filter can obtain higher precision in a short period of time.